# Modeling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps

## TL;DR

This paper introduces a novel SLV model with stochastic spot/variance correlation and Levy-driven drivers to capture the stochastic behavior of FX options' implied volatility skew, supported by a stable numerical scheme.

## Contribution

It develops a new SLV model with stochastic correlation driven by Levy processes and proposes a stable finite-difference scheme for calibration to market data.

## Key findings

- Model effectively captures stochastic skew in FX options
- Numerical scheme is unconditionally stable and second-order accurate
- Simulations demonstrate the model's capacity to fit market prices

## Abstract

It is known that the implied volatility skew of FX options demonstrates a stochastic behavior which is called stochastic skew. In this paper we create stochastic skew by assuming the spot/instantaneous variance correlation to be stochastic. Accordingly, we consider a class of SLV models with stochastic correlation where all drivers - the spot, instantaneous variance and their correlation are modeled by Levy processes. We assume all diffusion components to be fully correlated as well as all jump components. A new fully implicit splitting finite-difference scheme is proposed for solving forward PIDE which is used when calibrating the model to market prices of the FX options with different strikes and maturities. The scheme is unconditionally stable, of second order of approximation in time and space, and achieves a linear complexity in each spatial direction. The results of simulation obtained by using this model demonstrate capacity of the presented approach in modeling stochastic skew.